Vance County Schools GRADE 8 MATH 2015-2016 Pacing Guide UNIT STANDARDS NO. OF DAYS NINE WEEKS 1. Exponents & Scientific Notation 8.EE.1 8.EE.3 8.EE.4 12 2. Rational and Irrational Numbers 8.NS.1 8.NS.2 8.EE.2 10 3. One-Variable Linear Equations 8.EE.7 12 4. Pythagorean Theorem and Geometric Formulas 8.G.6 8.G.7 8.G.8 10 8.G.9 7 Benchmark A Week of November 7, 2016 5. Intro to Functions 8.EE.5 8.EE.6 8.F.2 8.F.5 6. Linear and Nonlinear Functions 8.F.1 8.F.3 8.F.4 16 7. Systems of Linear Equations 8.EE.8 15 Benchmark B Week of February 6, 2017 8. Geometric Transformation, 8.G.1 8.G.2 8.G.3 15 Congruence & Similarity 8.G.4 8.G.5 9. Bivariate Data & Linear Regression 8.SP.1 8.SP.2 8.SP.3 10 18 10. Two-Way Tables & Relative Frequencies Mock EOC Week of April 24, 2017 EOC Review for the remainder of the year 8.SP.4 10
Domain Testing Information Weight Distributions for 8 th Grade Math The Number System 2-7% Expressions & Equations 27-32% Functions 22-27% Geometry 20-25% Statistics and Probability 15-20% In addition to the content standards, the CCSS includes eight Standards for Mathematical Practice that cross domains, grade levels, and high school courses. Assessment items written for specific content standards will, as much as possible, also link to one or more of the mathematical practices. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
The pacing guide should be used along with the Common Core State Standards for Math and the NCDPI unpacking document Model and explain what positive and negative exponents mean Prove and explain the laws of exponents with positive, negative and zero exponents; especially raising powers and zero exponents Explain how to write numbers in correct scientific notation and explain why the first factor should be between -10 and 10 Model and explain how numbers can be written in scientific notation, converting between standard and scientific notation form Order and compare numbers in scientific form Give real world examples of very large and very small quantities and use scientific notation to describe the quantities Compare and contrast the size and magnitude of amounts using different units and justify the unit chosen in contextual situations Unit 1: Exponents and Scientific Notation 12 Days Standards: 8.EE.1, 8.EE.3, 8.EE.4 Laws of Exponents Power Perfect Squares Perfect Cubes Root Square Root Cube Root Magnitute Scientific Notation Standard Form Sample Questions * A baby hummingbird weighed about 4.4 10 3 pounds. A baby eastern bluebird weighed about 6.2 10 2 pounds. About how many times heavier was the baby eastern bluebird than the baby hummingbird? 8.EE.3 * What is the value of the expression (4 10 3 )(5.6 10 5 )? 8.EE.4 * What is the value of the expression (3 3 ) 2 3 4? 8.EE.1 * What is the value of (9.7 x 10 3 ) + (1.3 x 10 3 )? 8.EE.4 *One of the viruses that causes the common cold measures 2.5 10 6 m. What is this measurement written in standard form? 8.EE.3 * What is the product of 3.6 10 6 and 900,000,000 expressed in scientific notation? 8.EE.4 * What is the value of (3 2 ) (2 2 ) 2? 8.EE.1 * Lake Erie has a surface area of about 9.9 x 10 3 square miles. Lake Michigan has a surface area of about 2.2 x 10 4 square miles. About how many times larger is the surface area of Lake Michigan than the surface area of Lake Erie? 8.EE.3
Unit 2: Rational and Irrational Numbers 10 Days Standards: 8.NS.1, 8.NS.2, 8.EE.2 Make a graphic representation to show that natural numbers are a subset of whole numbers whole numbers are a subset of integers integers are a part of rational numbers rational and irrational numbers make up the set of real numbers Divide fractions to show that all rational numbers either repeat or terminate Change rational decimals to fractions Use long division to divide terminating decimals by factors to prove that terminating decimals have a prime factor of 2 or 5 Truncate decimals to get closer approximations and to order decimals Compare and order rational and irrational numbers; identify on the number line Model perfect square roots; prove that non-perfect square roots are irrational Explain why positive and negative numbers squared are positive but square roots can be positive or negative Recognize that squaring and taking the square root, cubing and taking the cube root, are inverse operations Real Numbers Irrational Numbers Rational Numbers Integers Whole Numbers Natural Numbers Radical Radicand Terminating Decimals Repeating Decimals Truncate s * Which letter is located at approximately on the number line below? 8.NS.2 * What is the value of? 8.EE.2 * 8.NS.1 * Jackson is comparing two squares. The first square has an area of 64 cm 2. The second square has an area of 121 cm 2. What is the difference in the perimeters of the two squares? 8.EE.2 * Which fraction is equivalent to? 8.NS.1 * What is the value of? 8.EE.2 *Sam stores his coin collection in a cube-shaped box that has a volume of 27 in. 3 He moves the coins into a larger cube-shaped box that has a volume of 729 in. 3 What is the difference between the edge lengths of the two boxes? 8.EE.2
Unit 3: One-Variable Linear Equations 12 Days Identify terms of expressions Model and prove the properties of equalities and properties of operations (e.g. distributive property) Write equations from word problems Transform an equation by utilizing the distributive property Transform and simplify an equation by combining like terms Transform and simplify an equation with variable on both sides Solve multi-step equation and justify each step; with rational and integer coefficients Standards: 8.EE.7a, b Sample Questions * The perimeter of the rectangle below is 48 feet. Expression Equation Constant Variable Coefficient Distributive Property What is the value of x? 8.EE.7b * What is the solution to the equation below? 8.EE.7a 0.5(9x + 18) = 1.5(5x) 2(3x + 4.5) * Three times the difference of a number, x, and fourteen is six times the sum of the same number, x, and twelve. What is the value of x? 8.EE.7b Like Terms Substitution Solution * What is the solution to the equation below? 8.EE.7a * A moving company offers two price plans. The first plan charges a flat rate of $39.95 plus $0.12 per mile driven. The second plans charges a flat rate of $19.95 plus $0.28 per mile driven. How many miles must the truck be driven for the two plans to cost the same? 8.EE.7b
Unit 4: Pythagorean Theorem & Geometric Formulas 17 days Use the Pythagorean Theorem to find unknown side lengths of right triangles Standards: 8.G.6, 8.G.7, 8.G.8, 8.G.9 Right Triangle * What is the approximate volume of the sphere below? Area? 8.G.9 Prove, model and explain the Pythagorean Theorem Identify Pythagorean triples Solve volume and surface area problems; apply Pythagorean Theorem if applicable Find the perimeter and area or two-dimensional figures on the coordinate plane Compare and contrast characteristics of cones, cylinders, and spheres and their formulas Describe, prove and solve problems using the formulas for cones, cylinders and spheres Hypotenuse Legs Pythagorean Theorem Pythagorean Triple Cone Cylinder Sphere Radius Diameter Volume Height Pi * Wendy has a rectangular flower garden that measures 20ft long and 10ft wide. She wants to construct a diagonal walkway through her garden. What is the approximate length of the walkway? 8.G.7 * Rectangle TUVW is shown to the right. What is the approximate length of the diagonal of rectangle TUVW? 8.G.8 * In the figure shown below, one square has side lengths of a units and the other square has side lengths of b units. The squares are divided into two triangles with a hypotenuse of c units. The pieces are rearranged to form a square with side length c. Which equation represents the relationship among the values of a, b, and c? 8.G.6
Unit 5: Intro to Functions 18 days Model and explain how x- and y-values in a function table are proportional Define unit rate, especially as it relates to a function table and a line on a graph Compare and contrast how proportional relationships are shown in graphs, tables, and equations Given an equation of a proportional relationship, graph the relationship and identify the unit rate Standards: 8.EE.5, 8.EE.6, 8.F.2, 8.F.5 Unit Rate Proportional Relationships Independent Variable Dependent Variable * Company R uses the formula C = 36 + 40h to calculate the cost, C, for doing h hours of work. Company S uses the table below to calculate their charges. Hours 1 3 7 Cost $80 $158 $314 Which company has the higher hourly rate, and by how much? 8.F.2 Compare and contrast two different proportional relationships represented two different ways (i.e. equation and table) Explain how changing the b value in an equation written in slope-intercept form changes the equations graph Graph lines in the forms y = mx and y = mx + b Model and define slope as the rate of change and the y-intercept as the initial value of a function, and explain how these help represent a function Determine the rate of change and the initial value from a description Find two points (two pairs of x- and y-values) from a table or graph and find the rate of change and initial value Slope Vertical Line Horizontal Slope-intercept Y- Intercept Linear Relationship Rate of Change Initial Value Function *The cost of a gallon of gasoline at Store M is represented by the equation y = 3.61x, where x is the number of gallons of gasoline and y is the total cost. The costs of gallons of gasoline at Store N are listed in the table below. Store N Gasoline Prices Gallons Total Cost 2 $7.16 4 $14.32 6 $21.48 What is the difference in the cost of a gallon of gasoline at the two stores? 8.EE.5 * Which graph shows the line of the equation 8.EE.6 * Bill and Sue save their leftover lunch money. Sue saves $5 a week. The equation m = 3.50w models the amount of money, m, Bill has saved after w weeks. At the end of 36 weeks, how much more money has Sue saved than Bill? 8.F.2
cont. Model and explain how to find the y-intercept from a table by finding what the y-value is when x = 0 Identify the initial value as the y-intercept in a real world situation cont. * Which is an equation of the line graphed below? 8.EE.6 Identify the rate of change in a real world situation (e.g. identify and discuss one time fees and repeated fees) Write an equation of a line in slope-intercept form from a real world situation Describe the shape of points or a group of connected points on a graph using the following vocabulary: Increasing or decreasing Model and explain how the points or lines on a graph show a relationship or action between the independent and dependent values Sketch a graph that relates the action taking place between two quantities in a scenario or situation Model and explain how to find slope from a table, equation or a graph Model and explain how the points or lines on a graph show a relationship or action between the independent and dependent values Sketch a graph that relates the action taking place between two quantities in a scenario or situation * A bus drives through Washington, D.C., allowing visitors to get off and on at various museums and monuments. Which graph best represents this situation? 8.F.5 * Sam leaves the park to walk home, but about halfway there he stops to talk to a friend. After talking to a friend for 5 minutes Sam continues home. Which graph represents Sam s walk home from the park? 8.F.5 * John was comparing the voltage of two circuits. The voltage, V, of Circuit 1 with a constant current can be represented by the equation V = 6R, where R represents the amount of resistance. The table below shows the voltage of Circuit 2 with a constant current and varying resistance 8.EE.5 Circuit 2 Resistance (R) Voltage (V) 3 12 5 20 10 40 Which is true of the graphs comparing voltage to resistance? A The graphs have the same slope. B The graph of Circuit 1 is steeper than the graph of Circuit 2. C The graph of Circuit 2 is steeper than the graph of Circuit 1. D The graph of Circuit 1 has a negative slope and the graph of Circuit 2 has a positive slope.
Unit 6: Linear and Nonlinear Functions 16 days Apply properties to model linear equations in different forms Model and identify functions as a set of ordered pairs satisfying one rule State and model the rule for functions as having exactly one y-value for any x-value Model x as input and y as output in ordered pairs, tables, and graphs Model and use the vertical line test to identify functions from graphs Identify and explain why a graph or table is not a function Describe the shape of points or a group of connected points on a graph using the following vocabulary: Linear or nonlinear Compare and contrast linear, quadratic, and exponential functions Identify functions from equations, graphs, ordered pairs, and tables List the properties of functions as equations and determine whether an equation represents a function, justifying why or why not Compare and contrast a linear equation in standard and y = mx + b form Make a table that represents a given graph or equation of a function Given a table, a graph, or a set of order pairs that is a linear function, write an equation for the function Write an equation for a line that passes through a given point and has a given slope Write an equation for a line that passes through two given points in slope-intercept form Standards: 8.F.1, 8.F.3, 8.F.4 Non-Linear Function Linear Function Input Output Rate of Change Linear Relationship Slope Standard Form Initial Value y-intercept Exponential Quadratic *Which set of ordered pairs represents a linear relationship? 8.F.3 A {(0, 1), (2, 2), ( 2, 0), (4, 3)} B {(0, 2), (1, 1), ( 1, 3), (2, 3)} C {(0, 1), (1, 1), ( 1, 2), (2, 3)} D {(0, 2.5), (5, 2.5), (1, 2.5), ( 1, 3.5)} * What is the equation of the line that passes through the origin and the point ( 1, 3)? 8.F.4 * Ryan paints the inside of houses to earn money. He charges a flat rate for supplies and a per room charge. To paint 3 rooms, Ryan charges $155. To paint 5 rooms, Ryan charges $225. How much does Ryan charge per room? 8.F.4 * Which equation is not a function? 8.F.1 A B C D * Which table of data shows a nonlinear function? 8.F.3
Unit 7: Systems of Linear Equations 15 days Model and explain that when two linear equations intersect on a line, the ordered pair of the point of intersection is a solution for both equations and that the x-value will generate the y-value Standards: 8.EE.8 Point of Interception Parallel Lines * A system of equations is shown below. Graph systems of equations to give solutions Model and compare using graphs and equations that systems of linear equations can have no solution, one solution, or infinitely many solutions Solve systems of equations with rational numbers Write systems of equations from word problems and explain the purpose of each variable, factor, and constant Use substitution to solve a system of equations Compare and contrast scenarios that are easier to interpret into a standard form equation with scenarios that are easier to interpret into a slopeintercept form equation Solve real world problems leading to two linear equations in two variables Graph two linear equations to determine whether they will intersect Coefficient Substitution No Solution Solution Infinitely Many Solutions Using the solution to the system, what is the value of x + y? * Lucas earns $7.50 per hour, and Ashley earns $8.00 per hour. Last week, Ashley worked 10 more hours than Lucas. The total amount Lucas and Ashley earned last week was $266. How many hours did Lucas work last week? * A store sells candy bars and packages of gum. The price of a candy bar is $0.69, and a package of gum costs $0.89. On Tuesday, the number of packages of gum sold was 2 less than 3 times the number of candy bars sold. The total amount of the sales was $82.22, before tax. How many packages of gum were sold? * Line m is graphed below. Line n will be graphed below. Line n will go through the points (1, 5) and ( 3, 3). What will be the point of intersection of lines m and n?
Unit 8: Geometric Transformation, Congruence & Similarity 15 days Define congruency and its symbol Define, describe, and perform rigid transformations Compare angles, side lengths, and parallel lines of pre-images and images after transformations have been performed Use appropriate tool (compass, protractor, rulers) to construct rigid transformations and prove their properties Define, describe and perform dilations, translations, reflections, rotations Identify the effect of each transformation on coordinates and state why Given a graph and coordinates of a reflection, identify the line of reflection; identify clock wise and counter-clockwise degrees of the rotation Construct two parallel lines with a transversal; identify alternate interior and exterior, corresponding, vertical, and adjacent angles; supplementary and complementary angles Given a graph or coordinates of pre-image and image, find scale factor of dilations Find missing angle measurements when two parallel lines are cut by two transversals to form a triangle Standards: 8.G.1, 8.G.2, 8.G.3, 8.G.4, 8.G.5 Translations Rotations Reflections Congruence Dilations Supplementary Complementary Angles: Exterior Interior Alternate Interior Vertical Adjacent * Triangle PQR has vertices at P( 5, 2), Q( 4, 5), and R( 3, 2). The triangle will be translated 6 units to the right and 5 units down. What will be the coordinates of Q?8.G.3 * In the figure below, lines j and k are parallel. What is the value of m? 8.G.5 * Triangle STU will be transformed to the points S ( 2, - 1), T (0, 5), and U (3, 1). What type of transformation will occur to triangle STU? 8.G.3 A reflection B rotation C dilation D translation
Unit 9: Bivariate Data & Linear Regression 10 days Use tools to generate data Graph bivariate date on a scatterplot by hand and with tools Explain why it is easier to change year dates into values of 0, 1, 2, etc. to write linear equations Examine and analyze scatterplots to determine and interpret and describe relationship (linear vs. nonlinear association, positive vs. negative association, and correlation vs. no correlation and strength of correlation) Identify outliers on a scatterplot and their effect on the line of best fit; interpret and describe their meaning in context Make predictions based on the graphed data and line of best fit Given a linear model that represents a scatter plot (line of best fit), write an equation for that line Interpret and describe the slope and intercepts of the equation of a linear model in the context of the bivariate measurement data Solve problems in the context of bivariate data Standards: 8.SP.1, 8.SP.2, 8.SP.3 Bivariate Data Scatter Plot Linear Model Line of Best Fit Linear Association Nonlinear Association Outliers Positive Association Negative Association Correlation Coefficient * The scatterplot below shows the average January temperatures for 10 cities compared to their latitude. Using a linear model, what is the predicted average January temperature for a city located at 30 North latitude? 8.SP.3 * Cameron surveyed students about the number of hours spent watching television each week, and the amount of allowance they received each week from their parents. His data is in the table below. Hours Watching TV 0 2 4 6 8 10 12 14 Allowance $20 $15 $10 $12 $10 $10 $5 $5 Which statement describes the association between the data? 8.SP.1 * The graph below shows the population of a town since 1950. Which equation best fits the data? 8.SP.2
Unit 10: Two-Way Tables & Relative Frequencies 10 days Collect bivariate categorical data from the same subjects and explain why both have to be collected from each subject Standards: 8.SP.4 Categorical Data Two-way Table * The table below shows the gender and grade of students in the band at a middle school. Construct a two-way table with categorical data collected by displaying frequencies and relative frequencies Interpret a two-way table and summarize the data Calculate relative frequencies to describe associations between two variables Solve problems by interpreting patterns of association and relative frequencies in bivariate categorical data from a two-way table Relative Frequency Bivariate Data Approximately what percent of the female students in the band are in the 8th grade? * A survey was conducted of 75 members of Mr. Smith s class to determine if they enjoy basketball and soccer. The results of the survey are shown in the table below. Based on the results of the survey, which statement is true? A Twenty-one of Mr. Smith s students do not enjoy basketball or soccer. B Forty of Mr. Smith s students enjoy basketball but do not enjoy soccer. C Thirty-two of Mr. Smith s students do not enjoy soccer. D Fifty-two of Mr. Smith s students enjoy basketball.